Subgroups — #20295923

Order 6976.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812773	C₂	1	2	yes	maximal, complemented
2	C₂×#13182012	C₂	1	1	yes	maximal, characteristic
3	#13182032	—	2	2	no	—
4	C₂×C₄×D₁₀₉	C₄	1	1	yes	characteristic
5	#13182012	—	2	2	no	—
6	C₂×#11724784	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
8	C₂²×D₁₀₉	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₀₉	C₈	1	1	yes	characteristic
11	C₄×D₁₀₉	—	2	1	no	—
12	C₄×D₁₀₉	—	2	1	no	—
13	C₈×C₁₀₉	—	2	1	no	—
14	#11724784	D₄	1	2	yes	—
15	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
16	C₂×D₁₀₉	—	2	1	no	—
17	C₂×D₁₀₉	—	4	1	no	—
18	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
20	Dic₁₀₉	—	2	1	no	—
21	C₂×C₁₀₉	—	2	1	no	—
22	C₂×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
23	D₁₀₉	—	4	1	no	—
24	C₁₀₉	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	109	1	no	maximal, Sylow
26	C₂×M₁₆	—	109	1	no	—
27	M₃₂	—	109	2	no	—
28	C₂²×C₄	—	109	1	no	—
29	M₁₆	—	218	2	no	—
30	C₂×C₈	—	109	1	no	—
31	C₂×C₈	#89137	1	1	yes	characteristic
32	C₁₆	—	218	2	no	—
33	C₂³	—	109	1	no	—
34	C₂×C₄	—	109	1	no	—
35	C₂×C₄	—	218	1	no	—
36	C₂×C₄	—	218	1	no	—
37	C₂×C₄	C₂×#89137	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	—	109	2	no	—
40	C₂²	—	436	1	no	—
41	C₂²	—	218	1	no	—
42	C₂²	D₁₀₉⋊C₈	1	1	yes	characteristic
43	C₄	—	218	1	no	—
44	C₄	C₂²⋊#89137	1	1	yes	characteristic
45	C₄	#13182039	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	436	1	no	—
48	C₂	#16812756	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#89137
commutator	C₂²×C₁₀₉	C₂×C₈
Frattini	C₂×C₄	C₂×#89137
Fitting	C₂×C₈×C₁₀₉	C₄
socle	C₂×C₁₀₉	C₂²⋊C₈
hypercenter	C₂×C₈	#89137
hypocenter	C₁₀₉	#349
LCS	G ▷ C₂²×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #16812773	C₂	semidirect
24. C₁₀₉	#349	semidirect